### Appendix A

A.1
This appendix includes a) details about the parameter settings for our simulator; b) simulator input data and related epidemic data resources; and c) our simulator source code and executed file, including detailed descriptions of parameter settings (i.e., external and estimated parameters).

#### Parameter Details

A.2
In this section, we thoroughly explain how we infer the parameters used in our model from R0 derived by other system dynamics researchers. Then we list the value of environmental and epidemical parameters of our simulator by way of tables.
##### Parameters Inferred from Statistical Data

A.3
In previous projects that used the compartmental model to simulate a contagious disease (Koopman 2004; Lipsitch et al. 2003; Riley et al. 2003), these projects reduced R0 to a simple relational expression A.1 (Anderson and May 1982; Becker 1992). In a situation where all of an infected individual's neighbors are susceptible, R0 = contact rate _ transmission probability _ duration of infection.

 (A.1)

A.4
After combining mirror identities with cellular automata, we modified the original expression A.1 to obtain another expression A.2.

 (A.2)

where Crate represents the rate of contact between an individual and his or her respective neighbors, Ctime the number of contacts between the individual and those neighbors in one day, Trate the average infected individual transmission rate, Tperiod the average infected individual transmission period, Avg. Mirror Identities the average number of mirror identities, and Num. of Neighbors the number of neighbors for each mirror identity.

A.5
Since we adopted the first layer of a Moore neighborhood for our simulation model, our Crate = 1/8 and Num. of Neighbors = 8. In addition to adopting R0 and transmission periods from epidemiologists, we adopted the average number of mirror identities and numbers of neighbors from sociologists, and then integrated R0-derived parameters to simulate a contagious disease and derive a transmission rate.

A.6
R0 is an epidemiological parameter derived from a system dynamics model. According to Lipsitch et al. (2003), Riley et al. (2003), Sebastian and Hoffmann (2003), and World Health Organization (2003), the SARS R0 fluctuated between 2.6 and 3.0 persons. Based on statistical data from national and municipal health authorities, we know that the average transmissible period (Tperiod) was between 4.5 and 6 days. We adopted the following values from sociologists: Avg. Mirror Identities = 3 and Num. of Neighbors = 8. After calculating these values, expression A.2 can be used to derive the Trate. A list of parameters used in our experiments is presented in Table A.1.
 Table A.1: Parameters used in the experiments R0 Crate Ctime Trate Tperiod Avg. Mirror Identities Num. of Neighbors SingaporeTaipeiToronto 2.7 1/8 4 0.045 5 3 8

A.7
We used Num. of Neighbors and Avg. Mirror Identities to build a two-dimensional simulator environment. Ctime, Crate, and Tperiod were used to determine individual transmission dynamics. R0 was used to derive the Trate, which was then used to determine individual transmission dynamics.

A.8
To validate our proposed model, we attempted to replicate an important R0 property: when R0 > 1, a disease is considered epidemic; when R0 = 1, the disease is described as endemic; when R0 < 1, the disease is easily suppressed. We believe that deconstructing R0 makes it possible to choose an effective suite of simulation parameters once epidemiologists determine a transmissible period value. Since parameter sensitivity to an epidemic model varies, R0 properties can be used to identify appropriate suites. In Figure A.1, the R0 properties are identifiable when Tperiod = 6, Avg. Mirror Identities = 3, and Ctime = 4. We divided our R0 into the six parameters that we used to build our model for performing a contagious disease simulation. We believe our model can also be used to display the epidemiological properties of R0.

 Figure A.1. Epidemic curves (R0 = 1.4, 1.0, and 0.6) when Tperiod = 6, Avg. Mirror Identities = 3, and Ctime = 4

#### Initial Global Environment Parameters

 Table A.2: Initial Global Environment Parameters Attribute Value Description P 100,000 Total number of agents. M 5 Upper limit of an agent's mirror identities. H 500 Height of the two-dimensional lattice used in the cellular automata. W 500 Width of the two-dimensional lattice used in the cellular automata. Avg. Mirror Identities 3 ~ 4 Average number of mirror identity. DayIncubation 5 Average number of incubation days. DayInfectious 25 Average number of infectious days. DayRecovered 7 Average number of recovered days. RateSuper 0.0001 Percentage of super-spreaders among total population. RateYoung 0.3 Percentage of young (0 to 20 years) agents in total population. RatePrime 0.5 Percentage of prime (21 to 60 years) agents in total population. RateOld 0.2 Percentage of old (60 years and above) agents in total population. RateInfection 0.045 Average infection rate. RateDeath 0.204 Average death rate.

### Input Epidemic Data And Related Resources

#### Singapore Simulation Input Data

 Table A.3: Singapore Simulation Input Data Time Step Action Persons State Public Health Policy Special Description on the Simulator 2003/3/1 Trigger 1 Infectious Super-spreader 2 Trigger 2 Infectious 11 Set Reducing Public Contact Efficacy = 0.9, Popularity = 0.5 15 Trigger 1 Incubation Wearing Mask Policy for Healthcare Worker Efficacy = 0.9, Popularity = 0.9 22 Trigger 2 Incubation 23 Set Home Quarantines 10 days, Popularity = 0.9 Controlling Hospital Access Efficacy = 0.9, Popularity = 0.9 Wearing Mask Policy for General Public Efficacy = 0.9, Popularity = 0.5 25 Trigger 2 Infectious 52 Set Taking Body Temperature Efficacy = 0.9, Popularity = 0.5

A.9
The efficacy level of each policy was set at 0.9. Popularity level was set at 0.9 for policies that were strictly enforced by government health authorities and at 0.5 for policies whose success depended on the cooperation of the general public without strict enforcement.

#### Taipei Simulation Input Data

We used what we learned from our Singapore experiment to simulate the spread of the SARS virus in Taipei. We used only those imported cases and health policies announced by the Taipei Municipal Department of Health.
 Table A.4: Taipei Simulation Input Data Time Step Action Persons State Public Health Policy Special Description on the Simulator 2003/3/20 Trigger 1 Infectious 2 Trigger 4 Incubation 9 Trigger 1 Incubation 11 Trigger 2 Infectious 12 Trigger 2 Infectious Home Quarantines 10 days, Popularity = 0.9 14 Trigger 1 Infectious 27 Trigger 1 Infectious Wearing Mask Policy for Healthcare Worker Efficacy = 0.9, Popularity = 0.9 47 Set Controlling Hospital Access Efficacy = 0.9, Popularity = 0.9 53 Set Home Quarantines 14 days, Popularity = 0.9 Wearing Mask Policy for General Public Efficacy = 0.9, Popularity = 0.5 74 Set Home Quarantines 10 days, popularity = 0.9 88 Set Taking Body Temperature Efficacy = 0.9, Popularity = 0.5

#### Toronto Simulation Input Data

 Table A.5: Toronto Simulation Input Data Time Step Action Persons State Public Health Policy Special Description on the Simulator 2003/2/23 Trigger 1 Infectious 6 Trigger 1 Infectious 19 Trigger 1 Infectious Wearing Mask Policy for Healthcare Worker Efficacy = 0.9, Popularity = 0.9 Reducing Public Contact Efficacy = 0.9, Popularity = 0.5 30 Trigger 1 Infectious 37 Set Controlling Hospital Access Efficacy = 0.9, Popularity = 0.9 Home Quarantines 10 days, Popularity = 0.9 38 Trigger 1 Infectious 68 Close All Public Health Policies opened before 91 Set Wearing Mask Policy for Healthcare Worker Efficacy = 0.9, Popularity = 0.9 112 Set All Public Health Policies closed before

### Simulator Source Code And Simulator File

A.10
Please send requests for our source code and simulator to gis89802@cis.nctu.edu.tw or gis91572@cis.nctu.edu.tw.

### References

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BECKER N G (1992) Infectious-Diseases of Humans - Dynamics and Control. Australian Journal of Public Health, 16, pp. 208-209.

KOOPMAN J (2004) Modeling infection transmission. Annual Review of Public Health 25: 303-26.

RILEY S, Fraser C, Donnelly C A, Ghani A C, Abu-Raddad L J, Hedley A J, Leung G M, Ho L M, Lam T H, Thach T Q, Chau P, Chan K P, Lo S V, Leung P Y, Tsang T, Ho W, Lee K H, Lau E M, Ferguson N M, and Anderson R M (2003) Transmission Dynamics of the Etiological Agent of SARS in Hong Kong: Impact of Public Health Interventions. Science, 300(5627), pp. 1961-1966.

LIPSITCH M, Cohen T, Cooper B, Robins J M, Ma S, James L, Gopalakrishna G, Chew S K, Tan C C, Samore M H, Fisman D, and Murray M (2003) Transmission Dynamics and Control of Severe Acute Respiratory Syndrome. Science, 300(5627), pp. 1966-1970.

SEBASTIAN B and Hoffmann C (2003) SARS Reference. Flying Publisher.

WHO (WORLD HEALTH ORGANIZATION) (2003) Consensus document on the epidemiology of severe acute respiratory syndrome (SARS), http://www.who.int/csr/sars/en/WHOconsensus.pdf.